Question

1. True or False: For a trigonometric function, y = f(x), then x = F-1(y). Explain your answer. (1 point)

2. True or False: For a one-to-one function, y = f(x), then x = f-1(y). Explain your answer. (1 point)

Answer 1

1. True
2. True

Explanation:

1. Since a capital letter (F) is used to show that the inverse equation is indeed a function, the question is true. If the inverse (second equation) was written as x=f-1(y), it would be false.

2. For one-to-one functions, all you need to do to reverse them is switch the x and y variables, and the
`f^-1` signifies that it is an inverse function.

Answer 2

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Answer:

1. False
2. True

Explanation:

If y = f(x) then x = f^-1(y) is true if and only if f(x) is a one-to-one function.

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1. False. Trig functions are periodic, so are not one-to-one.

2. True. The f(x) is specified as being one-to-one.